Import Question JSON

Current Question (ID: 20106)

Question:

$\text{A capacitance of } 2 \, \mu F \text{ is required in an electrical circuit across a potential difference of } 1.0 \, kV. \text{ A large number of } 1 \, \mu F \text{ capacitors are available which can withstand a potential difference of not more than } 300 \, V. \text{ The minimum number of capacitors required to achieve this is:}$ $1. \text{ 2}$ $2. \text{ 16}$ $3. \text{ 24}$ $4. \text{ 32}$

Options:

1. $2$
2. $16$
3. $24$
4. $32$

Solution:

$\text{Potential on each capacitor } V = \frac{1000}{n}$ $\frac{1000}{n} = 300$ $n = \frac{10}{3} \approx 4$ $C_{\text{eq}} = \frac{C}{n} \times m$ $\frac{1}{n} \times m = 2$ $m = n \times 2 = 4 \times 2 = 8$ $\text{Minimum number of capacitors} = 8 \times 4 = 32$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}